Conic sections Flashcards
(30 cards)
What are the four types of conic sections?
Circle, ellipse, parabola, hyperbola.
True or False: A circle is a type of ellipse.
True.
Fill in the blank: A parabola opens either _____ or _____.
upward, downward.
What is the standard form equation of a circle with center (h, k) and radius r?
(x - h)² + (y - k)² = r².
What is the general form of the equation of an ellipse?
(x²/a²) + (y²/b²) = 1.
Identify the conic section: x² + y² - 4x - 6y + 9 = 0.
Circle.
What is the definition of a hyperbola?
A set of points where the difference of the distances to two foci is constant.
True or False: The foci of a hyperbola are located along the transverse axis.
True.
What is the equation of a horizontal hyperbola?
(x²/a²) - (y²/b²) = 1.
Short answer: What is the directrix of a parabola?
A fixed line used in the definition of a parabola.
Fill in the blank: The major axis of an ellipse is the longest diameter that passes through the _____ and _____.
foci, center.
What is the eccentricity of a circle?
0.
Identify the conic section described: A set of all points in a plane equidistant from a point and a line.
Parabola.
What is the standard form of the equation for a vertical ellipse?
(x²/b²) + (y²/a²) = 1.
True or False: The vertices of a hyperbola are located at the endpoints of the conjugate axis.
False.
What do the terms ‘focus’ and ‘directrix’ relate to in conic sections?
They define the shape of conics, particularly parabolas.
What is the difference between a major axis and a minor axis in an ellipse?
The major axis is longer than the minor axis.
Fill in the blank: The distance between the foci of a hyperbola is _____ than the distance between the vertices.
greater.
What is the standard form of a parabola that opens to the right?
(y - k)² = 4p(x - h).
Identify the conic section: x² - 4y² = 16.
Hyperbola.
What is the formula for eccentricity (e) of an ellipse?
e = c/a, where c is the distance from the center to a focus.
True or False: All conic sections can be represented by second-degree polynomial equations.
True.
What does the term ‘latus rectum’ refer to in a parabola?
The line segment perpendicular to the axis of symmetry, passing through the focus.
Fill in the blank: The foci of an ellipse are located _____ the center.
inside.